Heterogeneity in behaviour and movement can influence the stability of predator–prey periodic travelling waves

Andrade, R. and Cobbold, C. A. (2023) Heterogeneity in behaviour and movement can influence the stability of predator–prey periodic travelling waves. Bulletin of Mathematical Biology, 85(1), 1. (doi: 10.1007/s11538-022-01101-8) (PMID:36418648)

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Cyclic predator–prey systems are often observed in nature. In a spatial setting, these can manifest as periodic traveling waves (PTW). Environmental change and direct human activity are known to, among other effects, increase the heterogeneity of the physical environment, which prey and predator inhabit. Aiming to understand the effects of heterogeneity on predator–prey PTWs, we consider a one-dimensional infinite landscape Rosenzweig–MacArthur reaction–diffusion model, with alternating patch types, and study the PTWs in this system. Applying the method of homogenisation, we show how heterogeneity can affect the stability of PTW solutions. We illustrate how the effects of heterogeneity can be understood and interpreted using Turchin’s concept of residence index (encapsuling diffusion rate and patch preference). In particular, our results show that prey heterogeneity acts to modulate the effects of predator heterogeneity, by this we mean that as prey increasingly spend more time in one patch type over another the stability of the PTWs becomes more sensitive to heterogeneity in predator movement and behaviour.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Antunes Costa de Andrade, Mr Renato and Cobbold, Professor Christina
Authors: Andrade, R., and Cobbold, C. A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Bulletin of Mathematical Biology
ISSN (Online):1522-9602
Published Online:23 November 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Bulletin of Mathematical Biology 85(1): 1
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
302369Insect abundance and climate variability: Novel insights from homogenisationChristina CobboldLeverhulme Trust (LEVERHUL)RF-2018-577\9M&S - Mathematics